%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN090-1.008 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:37:01 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.37s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 32
% Syntax : Number of formulae : 122 ( 36 unt; 0 def)
% Number of atoms : 264 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 287 ( 145 ~; 142 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of predicates : 32 ( 31 usr; 32 prp; 0-0 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s3_goal_1,axiom,
( ~ q_0
| ~ p_0 ),
file('theBenchmark.p',s3_goal_1) ).
cnf(c_1,plain,
( ~ q_0
| ~ p_0 ),
inference(clausify,[status(thm)],[s3_goal_1]) ).
fof(s3_type11_2,axiom,
( ~ q_2
| ~ q_1
| p_0 ),
file('theBenchmark.p',s3_type11_2) ).
cnf(c_3,plain,
( ~ q_2
| ~ q_1
| p_0 ),
inference(clausify,[status(thm)],[s3_type11_2]) ).
fof(s3_type11_4,axiom,
( ~ q_3
| ~ q_2
| p_1 ),
file('theBenchmark.p',s3_type11_4) ).
cnf(c_5,plain,
( ~ q_3
| ~ q_2
| p_1 ),
inference(clausify,[status(thm)],[s3_type11_4]) ).
fof(s3_type11_6,axiom,
( ~ q_4
| ~ q_3
| p_2 ),
file('theBenchmark.p',s3_type11_6) ).
cnf(c_7,plain,
( ~ q_4
| ~ q_3
| p_2 ),
inference(clausify,[status(thm)],[s3_type11_6]) ).
fof(s3_type11_8,axiom,
( ~ q_5
| ~ q_4
| p_3 ),
file('theBenchmark.p',s3_type11_8) ).
cnf(c_9,plain,
( ~ q_5
| ~ q_4
| p_3 ),
inference(clausify,[status(thm)],[s3_type11_8]) ).
fof(s3_type11_10,axiom,
( ~ q_6
| ~ q_5
| p_4 ),
file('theBenchmark.p',s3_type11_10) ).
cnf(c_11,plain,
( ~ q_6
| ~ q_5
| p_4 ),
inference(clausify,[status(thm)],[s3_type11_10]) ).
fof(s3_type11_12,axiom,
( ~ q_7
| ~ q_6
| p_5 ),
file('theBenchmark.p',s3_type11_12) ).
cnf(c_13,plain,
( ~ q_7
| ~ q_6
| p_5 ),
inference(clausify,[status(thm)],[s3_type11_12]) ).
fof(s3_type11_14,axiom,
( ~ q_8
| ~ q_7
| p_6 ),
file('theBenchmark.p',s3_type11_14) ).
cnf(c_15,plain,
( ~ q_8
| ~ q_7
| p_6 ),
inference(clausify,[status(thm)],[s3_type11_14]) ).
fof(s3_type11_16,axiom,
( ~ q_9
| ~ q_8
| p_7 ),
file('theBenchmark.p',s3_type11_16) ).
cnf(c_17,plain,
( ~ q_9
| ~ q_8
| p_7 ),
inference(clausify,[status(thm)],[s3_type11_16]) ).
fof(s3_type11_18,axiom,
( ~ q_10
| ~ q_9
| p_8 ),
file('theBenchmark.p',s3_type11_18) ).
cnf(c_19,plain,
( ~ q_10
| ~ q_9
| p_8 ),
inference(clausify,[status(thm)],[s3_type11_18]) ).
fof(s3_type11_20,axiom,
( ~ q_11
| ~ q_10
| p_9 ),
file('theBenchmark.p',s3_type11_20) ).
cnf(c_21,plain,
( ~ q_11
| ~ q_10
| p_9 ),
inference(clausify,[status(thm)],[s3_type11_20]) ).
fof(s3_type11_22,axiom,
( ~ q_12
| ~ q_11
| p_10 ),
file('theBenchmark.p',s3_type11_22) ).
cnf(c_23,plain,
( ~ q_12
| ~ q_11
| p_10 ),
inference(clausify,[status(thm)],[s3_type11_22]) ).
fof(s3_type11_24,axiom,
( ~ q_13
| ~ q_12
| p_11 ),
file('theBenchmark.p',s3_type11_24) ).
cnf(c_25,plain,
( ~ q_13
| ~ q_12
| p_11 ),
inference(clausify,[status(thm)],[s3_type11_24]) ).
fof(s3_type11_25,axiom,
( ~ p_14
| ~ p_13
| p_12 ),
file('theBenchmark.p',s3_type11_25) ).
cnf(c_26,plain,
( ~ p_14
| ~ p_13
| p_12 ),
inference(clausify,[status(thm)],[s3_type11_25]) ).
fof(s3_type11_27,axiom,
( ~ p_15
| ~ p_14
| p_13 ),
file('theBenchmark.p',s3_type11_27) ).
cnf(c_28,plain,
( ~ p_15
| ~ p_14
| p_13 ),
inference(clausify,[status(thm)],[s3_type11_27]) ).
fof(s3_type12_1,axiom,
( ~ q_2
| ~ p_1
| q_0 ),
file('theBenchmark.p',s3_type12_1) ).
cnf(c_30,plain,
( ~ q_2
| ~ p_1
| q_0 ),
inference(clausify,[status(thm)],[s3_type12_1]) ).
fof(s3_type12_3,axiom,
( ~ q_3
| ~ p_2
| q_1 ),
file('theBenchmark.p',s3_type12_3) ).
cnf(c_32,plain,
( ~ q_3
| ~ p_2
| q_1 ),
inference(clausify,[status(thm)],[s3_type12_3]) ).
fof(s3_type12_5,axiom,
( ~ q_4
| ~ p_3
| q_2 ),
file('theBenchmark.p',s3_type12_5) ).
cnf(c_34,plain,
( ~ q_4
| ~ p_3
| q_2 ),
inference(clausify,[status(thm)],[s3_type12_5]) ).
fof(s3_type12_7,axiom,
( ~ q_5
| ~ p_4
| q_3 ),
file('theBenchmark.p',s3_type12_7) ).
cnf(c_36,plain,
( ~ q_5
| ~ p_4
| q_3 ),
inference(clausify,[status(thm)],[s3_type12_7]) ).
fof(s3_type12_9,axiom,
( ~ q_6
| ~ p_5
| q_4 ),
file('theBenchmark.p',s3_type12_9) ).
cnf(c_38,plain,
( ~ q_6
| ~ p_5
| q_4 ),
inference(clausify,[status(thm)],[s3_type12_9]) ).
fof(s3_type12_11,axiom,
( ~ q_7
| ~ p_6
| q_5 ),
file('theBenchmark.p',s3_type12_11) ).
cnf(c_40,plain,
( ~ q_7
| ~ p_6
| q_5 ),
inference(clausify,[status(thm)],[s3_type12_11]) ).
fof(s3_type12_13,axiom,
( ~ q_8
| ~ p_7
| q_6 ),
file('theBenchmark.p',s3_type12_13) ).
cnf(c_42,plain,
( ~ q_8
| ~ p_7
| q_6 ),
inference(clausify,[status(thm)],[s3_type12_13]) ).
fof(s3_type12_15,axiom,
( ~ q_9
| ~ p_8
| q_7 ),
file('theBenchmark.p',s3_type12_15) ).
cnf(c_44,plain,
( ~ q_9
| ~ p_8
| q_7 ),
inference(clausify,[status(thm)],[s3_type12_15]) ).
fof(s3_type12_17,axiom,
( ~ q_10
| ~ p_9
| q_8 ),
file('theBenchmark.p',s3_type12_17) ).
cnf(c_46,plain,
( ~ q_10
| ~ p_9
| q_8 ),
inference(clausify,[status(thm)],[s3_type12_17]) ).
fof(s3_type12_19,axiom,
( ~ q_11
| ~ p_10
| q_9 ),
file('theBenchmark.p',s3_type12_19) ).
cnf(c_48,plain,
( ~ q_11
| ~ p_10
| q_9 ),
inference(clausify,[status(thm)],[s3_type12_19]) ).
fof(s3_type12_21,axiom,
( ~ q_12
| ~ p_11
| q_10 ),
file('theBenchmark.p',s3_type12_21) ).
cnf(c_50,plain,
( ~ q_12
| ~ p_11
| q_10 ),
inference(clausify,[status(thm)],[s3_type12_21]) ).
fof(s3_type12_23,axiom,
( ~ q_13
| ~ p_12
| q_11 ),
file('theBenchmark.p',s3_type12_23) ).
cnf(c_52,plain,
( ~ q_13
| ~ p_12
| q_11 ),
inference(clausify,[status(thm)],[s3_type12_23]) ).
fof(s3_type12_26,axiom,
( ~ p_14
| ~ q_13
| q_12 ),
file('theBenchmark.p',s3_type12_26) ).
cnf(c_55,plain,
( ~ p_14
| ~ q_13
| q_12 ),
inference(clausify,[status(thm)],[s3_type12_26]) ).
fof(s3_type12_27,axiom,
( ~ q_15
| ~ p_14
| q_13 ),
file('theBenchmark.p',s3_type12_27) ).
cnf(c_56,plain,
( ~ q_15
| ~ p_14
| q_13 ),
inference(clausify,[status(thm)],[s3_type12_27]) ).
fof(t3_1,axiom,
p_14,
file('theBenchmark.p',t3_1) ).
cnf(c_62,plain,
p_14,
inference(clausify,[status(thm)],[t3_1]) ).
fof(t3_2,axiom,
p_15,
file('theBenchmark.p',t3_2) ).
cnf(c_63,plain,
p_15,
inference(clausify,[status(thm)],[t3_2]) ).
fof(t3_4,axiom,
q_15,
file('theBenchmark.p',t3_4) ).
cnf(c_65,plain,
q_15,
inference(clausify,[status(thm)],[t3_4]) ).
cnf(c_97,plain,
( ~ q_15
| q_13 ),
inference(resolve,[status(thm)],[c_62,c_56]) ).
cnf(c_66,plain,
q_13,
inference(resolve,[status(thm)],[c_65,c_97]) ).
cnf(c_98,plain,
( ~ p_14
| q_12 ),
inference(resolve,[status(thm)],[c_66,c_55]) ).
cnf(c_67,plain,
q_12,
inference(resolve,[status(thm)],[c_62,c_98]) ).
cnf(c_99,plain,
( ~ p_15
| p_13 ),
inference(resolve,[status(thm)],[c_62,c_28]) ).
cnf(c_68,plain,
p_13,
inference(resolve,[status(thm)],[c_63,c_99]) ).
cnf(c_100,plain,
( ~ p_14
| p_12 ),
inference(resolve,[status(thm)],[c_68,c_26]) ).
cnf(c_69,plain,
p_12,
inference(resolve,[status(thm)],[c_62,c_100]) ).
cnf(c_101,plain,
( ~ q_13
| q_11 ),
inference(resolve,[status(thm)],[c_69,c_52]) ).
cnf(c_70,plain,
q_11,
inference(resolve,[status(thm)],[c_66,c_101]) ).
cnf(c_102,plain,
( ~ q_13
| p_11 ),
inference(resolve,[status(thm)],[c_67,c_25]) ).
cnf(c_71,plain,
p_11,
inference(resolve,[status(thm)],[c_66,c_102]) ).
cnf(c_103,plain,
( ~ q_12
| q_10 ),
inference(resolve,[status(thm)],[c_71,c_50]) ).
cnf(c_72,plain,
q_10,
inference(resolve,[status(thm)],[c_67,c_103]) ).
cnf(c_104,plain,
( ~ q_12
| p_10 ),
inference(resolve,[status(thm)],[c_70,c_23]) ).
cnf(c_73,plain,
p_10,
inference(resolve,[status(thm)],[c_67,c_104]) ).
cnf(c_105,plain,
( ~ q_11
| q_9 ),
inference(resolve,[status(thm)],[c_73,c_48]) ).
cnf(c_74,plain,
q_9,
inference(resolve,[status(thm)],[c_70,c_105]) ).
cnf(c_106,plain,
( ~ q_11
| p_9 ),
inference(resolve,[status(thm)],[c_72,c_21]) ).
cnf(c_75,plain,
p_9,
inference(resolve,[status(thm)],[c_70,c_106]) ).
cnf(c_107,plain,
( ~ q_10
| q_8 ),
inference(resolve,[status(thm)],[c_75,c_46]) ).
cnf(c_76,plain,
q_8,
inference(resolve,[status(thm)],[c_72,c_107]) ).
cnf(c_108,plain,
( ~ q_10
| p_8 ),
inference(resolve,[status(thm)],[c_74,c_19]) ).
cnf(c_77,plain,
p_8,
inference(resolve,[status(thm)],[c_72,c_108]) ).
cnf(c_109,plain,
( ~ q_9
| q_7 ),
inference(resolve,[status(thm)],[c_77,c_44]) ).
cnf(c_78,plain,
q_7,
inference(resolve,[status(thm)],[c_74,c_109]) ).
cnf(c_110,plain,
( ~ q_9
| p_7 ),
inference(resolve,[status(thm)],[c_76,c_17]) ).
cnf(c_79,plain,
p_7,
inference(resolve,[status(thm)],[c_74,c_110]) ).
cnf(c_111,plain,
( ~ q_8
| q_6 ),
inference(resolve,[status(thm)],[c_79,c_42]) ).
cnf(c_81,plain,
q_6,
inference(resolve,[status(thm)],[c_76,c_111]) ).
cnf(c_112,plain,
( ~ q_8
| p_6 ),
inference(resolve,[status(thm)],[c_78,c_15]) ).
cnf(c_82,plain,
p_6,
inference(resolve,[status(thm)],[c_76,c_112]) ).
cnf(c_113,plain,
( ~ q_7
| q_5 ),
inference(resolve,[status(thm)],[c_82,c_40]) ).
cnf(c_84,plain,
q_5,
inference(resolve,[status(thm)],[c_78,c_113]) ).
cnf(c_114,plain,
( ~ q_7
| p_5 ),
inference(resolve,[status(thm)],[c_81,c_13]) ).
cnf(c_85,plain,
p_5,
inference(resolve,[status(thm)],[c_78,c_114]) ).
cnf(c_115,plain,
( ~ q_6
| q_4 ),
inference(resolve,[status(thm)],[c_85,c_38]) ).
cnf(c_86,plain,
q_4,
inference(resolve,[status(thm)],[c_81,c_115]) ).
cnf(c_116,plain,
( ~ q_6
| p_4 ),
inference(resolve,[status(thm)],[c_84,c_11]) ).
cnf(c_87,plain,
p_4,
inference(resolve,[status(thm)],[c_81,c_116]) ).
cnf(c_117,plain,
( ~ q_5
| q_3 ),
inference(resolve,[status(thm)],[c_87,c_36]) ).
cnf(c_88,plain,
q_3,
inference(resolve,[status(thm)],[c_84,c_117]) ).
cnf(c_118,plain,
( ~ q_5
| p_3 ),
inference(resolve,[status(thm)],[c_86,c_9]) ).
cnf(c_89,plain,
p_3,
inference(resolve,[status(thm)],[c_84,c_118]) ).
cnf(c_119,plain,
( ~ q_4
| q_2 ),
inference(resolve,[status(thm)],[c_89,c_34]) ).
cnf(c_90,plain,
q_2,
inference(resolve,[status(thm)],[c_86,c_119]) ).
cnf(c_120,plain,
( ~ q_4
| p_2 ),
inference(resolve,[status(thm)],[c_88,c_7]) ).
cnf(c_91,plain,
p_2,
inference(resolve,[status(thm)],[c_86,c_120]) ).
cnf(c_121,plain,
( ~ q_3
| q_1 ),
inference(resolve,[status(thm)],[c_91,c_32]) ).
cnf(c_92,plain,
q_1,
inference(resolve,[status(thm)],[c_88,c_121]) ).
cnf(c_122,plain,
( ~ q_3
| p_1 ),
inference(resolve,[status(thm)],[c_90,c_5]) ).
cnf(c_93,plain,
p_1,
inference(resolve,[status(thm)],[c_88,c_122]) ).
cnf(c_123,plain,
( ~ q_2
| q_0 ),
inference(resolve,[status(thm)],[c_93,c_30]) ).
cnf(c_94,plain,
q_0,
inference(resolve,[status(thm)],[c_90,c_123]) ).
cnf(c_124,plain,
( ~ q_2
| p_0 ),
inference(resolve,[status(thm)],[c_92,c_3]) ).
cnf(c_95,plain,
p_0,
inference(resolve,[status(thm)],[c_90,c_124]) ).
cnf(c_125,plain,
~ q_0,
inference(resolve,[status(thm)],[c_95,c_1]) ).
cnf(c_96,plain,
$false,
inference(resolve,[status(thm)],[c_94,c_125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN090-1.008 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n010.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Sat Sep 26 17:11:01 UTC 2026
% 0.07/0.33 % CPUTime :
% 0.07/0.33 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.33 % Process 3785205 was started by sandbox2 on n010,
% 0.07/0.33 % Sat Sep 26 17:11:01 2026
% 0.07/0.33 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/0.34
% 0.07/0.34 % From the command line: assign(max_seconds, 300).
% 0.07/0.37
% 0.07/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.37
% 0.07/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.07/0.37 % Length of proof is 61.
% 0.07/0.37 % Level of proof is 15.
% 0.07/0.37 % Maximum clause weight is 3.000.
% 0.07/0.37 % Given clauses 0.
% 0.07/0.37
% 0.07/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------